But what is the equivalent if I have 3 molecules and a single excitation? i.e. I now start with the states [itex]\left| E_{1} G G\right\rangle[/itex], [itex]\left| G E_{2} G\right\rangle[/itex] and [itex]\left| G G E_{3} \right\rangle[/itex], and want to rewrite them?

I think one of the new states should be [itex]\frac{\left(\left| E_{1} G G\right\rangle + \left| G E_{2} G\right\rangle + \left| G G E_{3} \right\rangle \right)}{√3}[/itex], but I'm not sure about the others?